Uniqueness in a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity

• URL: http://arxiv.org/abs/2109.14083v3
• Date: Thu, 31 Mar 2022 07:20:45 GMT
• Title: Uniqueness in a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity
• Authors: Pranava Chaitanya Jayanti, Konstantina Trivisa
• Abstract summary: We prove a weak-strong type uniqueness theorem for weak solutions of Navier-Stokes equations. Only some of their regularity properties are used, allowing room for improved existence theorems in the future.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a previous paper [Jayanti, P.C., Trivisa, K. Local Existence of Solutions to a Navier-Stokes-Nonlinear-Schr\"odinger Model of Superfluidity. J. Math. Fluid Mech. 24, 46 (2022)], the authors proved the existence of local-in-time weak solutions to a model of superfluidity. The system of governing equations was derived by Pitaevskii in 1959 and couples the nonlinear Schr\"odinger equation (NLS) and the Navier-Stokes equations (NSE). In this article, we prove a weak-strong type uniqueness theorem for these weak solutions. Only some of their regularity properties are used, allowing room for improved existence theorems in the future, with compatible uniqueness results.

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